Problem: Which of the following numbers is a factor of 126? ${5,10,11,12,14}$
Explanation: By definition, a factor of a number will divide evenly into that number. We can start by dividing $126$ by each of our answer choices. $126 \div 5 = 25\text{ R }1$ $126 \div 10 = 12\text{ R }6$ $126 \div 11 = 11\text{ R }5$ $126 \div 12 = 10\text{ R }6$ $126 \div 14 = 9$ The only answer choice that divides into $126$ with no remainder is $14$ $ 9$ $14$ $126$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $14$ are contained within the prime factors of $126$ $126 = 2\times3\times3\times7 14 = 2\times7$ Therefore the only factor of $126$ out of our choices is $14$. We can say that $126$ is divisible by $14$.